POPULATION INVARIANCE AND THE EQUATABILITY OF TESTS: BASIC THEORY AND THE LINEAR CASE

Abstract

Equating functions are supposed to be population invariant by definition. But when two tests are not equatable, it is possible that the linking functions, used to connect the scores of one to the scores of the other, are not invariant across different populations of examinees. We introduce two root-mean-square difference measures of the degree to which linking function are different for different subpopulations. We also introduce the system of “parallel-linear” linking functions for multiple subpopulations and show that, for this system, our measure of population invariance can be easily computed from the standardized mean differences between the scores of the subpopulations on the two tests. For the parallel-linear case, we develop a correlation-based upper bound on our measure.